The (branches) of my Yucca are bending downward and contorting

If you have a yucca like the one in the picture, https://www.gardeningknowhow.com/ornamental/foliage/yucca/growing-yucca-indoors.htm
your problem is probably that the soil has been too moist for too long and the roots have been damaged. No matter what kind of yucca you have, I would guess the problem most likely to be associated with the roots. Try to get the plant out of the pot it's in, cut away any damaged roots, and put it into a slightly larger pot with drainage holes and good draining, coarse potting mix. https://www.gardeningknowhow.com/plant-problems/disease/treating-root-rot-gardening-tips-for-housplants.htm
A word of caution, though. If the rot has extended to the branches, so that they are soft, there's probably nothing you can do to save the plant. Try again with another one, and let the soil dry between waterings until it is only slightly damp; test the soil near the bottom of the pot to determine the moisture level; and keep the yucca in high light.